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Geometry of Poisson structures
Georgian Mathematical Journal, 1995Abstract The purpose of this paper is to consider certain mechanisms of the emergence of Poisson structures on a manifold. We shall also establish some properties of the bivector field that defines a Poisson structure and investigate geometrical structures on the manifold induced by such fields.
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Poisson Geometry and Applications
Oberwolfach Reports, 2008The half-size workshop was organized by Anton Alekseev (Geneve), Rui Loja Fernandes (Lisboa), Eckhard Meinrenken (Toronto) and Markus Pflaum (Frankfurt). Marius Crainic (Utrecht) also acted as an unofficial organizer. The programme consisted of 17 lectures and covered a range of areas in Poisson Geometry and its applications where significant progress ...
Anton Alekseev +3 more
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Special Symplectic Connections and Poisson Geometry
Letters in Mathematical Physics, 2004The authors show how any special symplectic connection can be constructed using symplectic realizations of quadratic deformations of a certain linear Poisson structure. The space of symplectic connections is rather huge. Therefore, to study meaningful connections, it is thus necessary to impose further conditions. In this paper, the authors investigate
Cahen, Michel, Schwachhöfer, Lorenz J.
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Generalizing Poisson Algebra with Geometry
JPS Hot Topics, 2021Using a differential geometric interpretation of Hamiltonian mechanics, a generalized Poisson bracket formulation is developed for a three-dimensional phase space characterized by a triplet of canonical variables.
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Noncommutative geometry of Poisson structures
Journal of Mathematical Sciences, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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